How quickly will a comet evaporate?

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Question

How long does it take for a comet to completely 'melt' away from repeated exposures to the Sun? (Composition and size would certainly have something to do with it, I'm sure) Will there come a time when all the comets are gone from the Solar System because they have sublimated?

Answer

We put this question to Dr Jonathan Shanklin, director of the Comet sections of the British Astronomical Association and the Society for Popular Astronomy...